**Math
5710 Introduction to Applied Mathematics **

M W F 11:50 am - 12:40 pm JTB 320

** **Mathematics is the Queen that rules the Universe

Office: LCB 206
ph:
801-581-7315 email: elena@math.utah.edu Office hours: W 1-2 pm and by
appointmentClass
webpage: http://www.math.utah.edu/~elena/M5710/5710.html |

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*** practice test

Sample problems:

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Show all work (No work shown => No credit given)

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Hw1 (due Sept. 6): 1.4.10, 1.4.11, 1.4.15, 1.4.2

sect. 1.3: ## 8, 11, 12, 20; sect. 1.4: ## 2, 6, 7, 8

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Hw2 (due Sept. 20): sect. 2.1: # 2, 5; sect. 2.2: # 1, 3

sect. 2.2: # 7, 10, 11, 12, 14

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Hw3 (due Oct. 4/6): sect. 2.3: # 1, 2, 3, 9, 11

sect. 2.4: # 2, 5, 7, 10, 11, 12

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Hw4 (due Oct. 18): sect. 3.1: # 1, 4, 5, 12, 13 delta-function

sect. 3.1: # 6, 15, 16. Sect. 3.2: # 1, 2

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Hw5 (due Nov. 3): sect. 3.2: # 3, 4, 6, 7, 8, 10, 11

sect. 3.3: # 1, 2, 6

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Hw6 (due Nov. 15): sect. 3.3: # 7, 8, 9, 11, 12, 13, 14, 16, 17, 19 ---------------------------------------------------------------------------------------------

Hw7 (due Nov. 29): sect. 3.4: # 2, 3, 4, 5, 8, 10, 18, 19

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Hw8 (due Dec. 13): sect. 3.4: # 23, 24, 34

sect. 3.5: # 2, 3, 4, 7, 8, 15, 23

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Aug 21-27: We start with a model of a spring/mass chain (sect. 1.4, Ex. 2, pp. 40-41) to continue next time and talk about a fundamental principle of the minimum of the potential energy (sect. 1.4). We will also discuss least squares solutions to linear problems.

Aug 28-Sept 1: M, F - Electric networks. W - No lecture. Refresh linear algebra (ch. 1).

Sept 4-8: W, F - Lagrange multipliers (sect. 2.2)

Sept 11-15: We discuss duality and its applications

Sept 18-22: We will talk about electrical networks and minimum principles (sect. 2.3) and then continue with networks of elastic bars or trusses (sect. 2.4)

Sept 25-29: We discuss structures in equilibrium (sect. 2.4). A particular example of such a structure is a truss made of elastic bars connected by hinges. We also start to talk about equilibrium in the continuous case for a one-dimensional problem (sect. 3.1).

Oct 2-6: We discuss equilibrium in continuous one-dimensional problems, Sturm- Liouville problems, regular and singular perturbations (sect. 3.1).

Oct 9-13: Fall break

Oct 16-20: We talk about delta function and discuss differential equations of equilibrium (sect. 3.2).

Oct 23-27: We continue to discuss equations of equilibrium, minimum principles, duality for one-dimensional problems such as stretching or bending of a beam (sect. 3.2).

Oct 30-Nov 3: This week we discuss two-dimensional Laplace's equation (section 3.3) and potential or irrotational flows.

Nov 6-10: We start to discuss three-dimensional problems, cross-product, curl, and relations between curl, grad, and div operators (sect. 3.4).

Nov 13-22: Continue with three-dimensional problems, Maxwell's equations (sect. 3.4).

Nov 27-Dec 1: We discussion of the Maxwell's equations and three-dimensional flows (sect. 3.4). We also start to talk about solids (sect. 3.5).

Dec 4-6: Equilibrium of solids and fluids (sect. 3.5).

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Optimality and duality is another focus of the course
(and another best part of modern applied mathematics), which expresses
itself as a fundamental principle of energy minimization (or
stationarity of the energy). This principle governs all the processes in
the world, and we will see mathematical justification of that through
the same mathematical framework held for all the problems and topics
discussed in the course.

Particular covered topics include optimization and
duality, partial differential equations (potential flows, electricity
and magnetism, equilibrium of fluids and solids, heat equation versus
wave equation), ordinary differential equations (stability, chaos
and fractals, nonlinear conservation laws), networks (electric,
mechanic, social, internet) and transportation problem.

About the textbook:
*Renowned mathematician Gilbert Strang teaches applied
mathematics with the clear explanations, examples and insights
of an experienced teacher. This book progresses steadily
through a range of topics from symmetric linear systems to
differential equations to least squares and optimization. It
clearly demonstrates the power of matrix algebra in
engineering problem solving. This is an ideal book (beloved by
many readers) for a first course on applied mathematics and a
reference for more advanced applied mathematicians. The only
prerequisite is a basic course in linear algebra. /Google
books/***
Table of Contents:** http://www-math.mit.edu/~gs/books/itam_toc.html

**Exams:** There will be two midterms, project, and a final exam.

**Final: **Wednesday, December 13, 2017, 10:30 am – 12:30 pm**
**

**
Grading:** The grade will be based on the
homework (20%) and project and the exams
(80%). You are welcome to work on the homework problems together
with other students, but you have to write your own solutions.

**Holidays****: **Labor Day holiday:
Monday, September 4;

Thanksgiving break:
Thurs.-Fri., Nov. 23-24.

Fall break:
October 8-15.